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3D Seed Placement The placement of seeds directly determines the visualization quality – Too many: scene cluttering – Too little: no pattern formed It has to be in the right place and in the right amount

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streamribbon: a ribbon (surface of fixed width) always tangent to the vector field shows rotational (or twist) properties of the 3D flow

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Streamribbon generation: Start with a 3D point x i=0 and a 2 nd one y i=0 in a particular dist. d, i.e. |x i -y i |² = d² Loop: Integrate from x i to yield x i+1 Do an integration step from y i to yield z renormalize the distance between x i+1 & z to d, i.e. y i+1 = x i+1 + d·(z-x i+1 )/|z-x i+1 | End streamribbon integration if necessary

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The computation of stream surfaces is similar to streamribbon. However, now the seeding points are typically more than two. Also, during the integration, we may need to adaptively add or remove seeds (i.e. handling divergence, convergence, and shear). Triangulating the stream surface between neighboring streamlines is easy to achieve. What is the challenge? What about Stream Surfaces?

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Where to put seeds to start the integration? Seeding along a straight-line Allow user exploration [Weiskopf et al. 2007] Seeding along the direction that is perpendicular to the flow leads to stream surface with large coverage [Edmunds et al. EuroVis2012]

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How about automatic stream surface placement? Where to start? How to proceed? [Edmunds et al. TPCG 2012] Render

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Saddle Connectors Flow behind a circular cylinder: 13 fixed points and 9 saddle connectors have been detected and visualized. Additional LIC planes have been placed to show the correspondence between the skeleton and the flow. Source: Theisel et al. 2003